• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site

Book

THE MOST PROBABLE PATHS FOR DIFFUSIONS WITH JUMPS

12th International Vilnius Conference on Probability Theory and Mathematical Statistics, 2018.

We generalize well-known results on the Onsager–Machlup functional for diffusions. The
case of L´evy processes with finite number of jumps and diffusions with jumps were considered
in our work. The Onsager–Machlup functional of a c´adl´ag process X is defined
by the following expression
OM( f ,ψ) = lim_{ε→0}P{ω : ||X(ω)− f|| <ε }/P{ω : ||X(ω)−ψ|| <ε },
where || · || is a norm in the Skorokhod space D[0,∞]. This expression gives a tool to
compare weights of trajectories of the corresponding process, also it is naturally connected
with the most probable sample path of the process. This interpretation leads to the
number of applications, for example, to the popular Customer Journey Maps problem.









THE MOST PROBABLE PATHS FOR DIFFUSIONS WITH JUMPS